A state space represents a problem in
terms of states and operators that change states.

A state space consists of:

A representation of the states the system can be in.
In a board game, for example, the board represents the current
state of the game.

A set of operators that can change one state into
another state. In a board game, the operators
are the legal moves from any given state. Often
the operators are represented as programs that
change a state representation to represent the new state.

An initial state.

A set of final states; some of these may be
desirable, others undesirable.
This set is often represented implicitly by a
program that detects terminal states.